Free Compass Math Practice on Mean, Median and Mode Solutions with Full Explanations

The mean is equal to the sum of all data values divided by the number of data values.

mean = (10.2 + 10.5 + 10.9 + 10.2 + 10.6 + 10.0) / 6 = 10.4

Which of the statements, related to the mean, mode and median of the data set given below is true?

12 , 15 , 10 , 19 , 5 , 5

A) the mean is equal to the median
B) the mode is larger than the mean
C) the median is smaller than the mode
D) the above data set has two modes
E) The median of the above data is equal to 14.5

Solution

The mean is equal to the sum of all data values divided by the number of data values.

(12 + 15 + 10 + 19 + 5 + 5) / 6 = 11

Mode: First arrange data from smallest to largest

5 , 5 , 10 , 12 , 15 , 19

Median is the data value in the middle of the ordered data set. Since the number of data values is even there is no single data value in the middle of the set and therefore the median is equal to the average of the two data values in the middle

median = (10 + 12) / 2 = 11

Mode is the data value with highest frequency of repetition.

mode = 5

Examining the value of the mean, median and mode, the statement in A) "the mean is equal to the median" is correct.

All the data set given above have 5 data values. The mean is equal to the sum of all data values divided by the number of data values. For the mean to be less than 100, the sum of all data values in a given set must be less than 5*100 = 500. Let us find the sum of all data values in all 5 sets given above: